Reconstruction of Incomplete Data Sets orImages Using Direct Sampling

With increasingly sophisticated acquisition methods, the amount of data available for mapping physical parameters in the geosciences is becoming enormous. If the density of measurements is sufficient, significant non-parametric spatial statistics can be derived from the data. In this context, we propose to use and adapt the Direct Sampling multiple-points simulation method (DS) for the reconstruction of partially informed images. The advantage of the proposed method is that it can accommodate any data disposition and that it can indifferently deal with continuous and categorical variables. The spatial patterns found in the data are mimicked without model inference. Therefore, very few assumptions are required to define the spatial structure of the reconstructed fields, and very limited parameterization is needed to make the proposed approach extremely simple from a user perspective. The different examples shown in this paper give appealing results for the reconstruction of complex 3D geometries from relatively small data set

Extrapolating the Fractal Characteristics of an Image Using Scale-Invariant Multiple-Point Statistics

The resolution of measurement devices can be insufficient for certain purposes. We propose to stochastically simulate spatial features at scales smaller than the measurement resolution. This is accomplished using multiple-point geostatistical simulation (direct sampling in the present case) to interpolate values at the target scale. These structures are inferred using hypothesis of scale invariance and stationarity on the spatial patterns found at the coarse scale. The proposed multiple-point super-resolution mapping method is able to deal with "both continuous and categorical variables,” and can be extended to multivariate problems. The advantages and limitations of the approach are illustrated with examples from satellite imagin

Hydrological characterization of cave drip waters in a porous limestone: Golgotha Cave, Western Australia

Cave drip water response to surface meteorological conditions is complex due to the heterogeneity of water movement in the karst unsaturated zone. Previous studies have focused on the monitoring of fractured rock limestones that have little or no primary porosity. In this study, we aim to further understand infiltration water hydrology in the Tamala Limestone of SW Australia, which is Quaternary aeolianite with primary porosity. We build on our previous studies of the Golgotha Cave system and utilize the existing spatial survey of 29 automated cave drip loggers and a lidar-based flow classification scheme, conducted in the two main chambers of this cave. We find that a daily sampling frequency at our cave site optimizes the capture of drip variability with the least possible sampling artifacts. With the optimum sampling frequency, most of the drip sites show persistent autocorrelation for at least a month, typically much longer, indicating ample storage of water feeding all stalactites investigated. Drip discharge histograms are highly variable, showing sometimes multimodal distributions. Histogram skewness is shown to relate to the wetter-than-average 2013 hydrological year and modality is affected by seasonality. The hydrological classification scheme with respect to mean discharge and the flow variation can distinguish between groundwater flow types in limestones with primary porosity, and the technique could be used to characterize different karst flow paths when high-frequency automated drip logger data are available. We observe little difference in the coefficient of variation (COV) between flow classification types, probably reflecting the ample storage due to the dominance of primary porosity at this cave site. Moreover, we do not find any relationship between drip variability and discharge within similar flow type. Finally, a combination of multidimensional scaling (MDS) and clustering by k means is used to classify similar drip types based on time series analysis. This clustering reveals four unique drip regimes which agree with previous flow type classification for this site. It highlights a spatial homogeneity in drip types in one cave chamber, and spatial heterogeneity in the other, which is in agreement with our understanding of cave chamber morphology and lithology. © Author(s) 201

Analog-based meandering channel simulation

Characterizing the complex geometries and the heterogeneity of the deposits in meandering river systems is a long-standing issue for the 3-D modeling of alluvial formations. Such deposits are important sources of accessible groundwater in alluvial aquifers throughout the world and also play a major role as hydrocarbons reservoirs. In this paper, we present a method to generate meandering river centerlines that are stochastic, geologically realistic, connected, and conditioned to local observations or global geomorphological characteristics. The method is based on fast 1-D multiple-point statistics in a transformed curvilinear domain: the succession in directions observed in a real-world meandering river (the analog) is considered as statistical model for multiple-point statistics simulation. The integration of local data is accomplished by an inverse procedure ensuring that the channels pass through a given set of locations while conserving the high-order spatial characteristics of an analog. The methodology is applied on seven real-world case studies. This work demonstrates the flexibility and the applicability of multiplepoint statistics outside the standard paradigm that considers the simulation of a 2-D or 3-D variable with spatial coordinates

High resolution multi-facies realizations of sedimentary reservoir and aquifer analogs

Geological structures are by nature inaccessible to direct observation. This can cause difficulties in applications where a spatially explicit representation of such structures is required, in particular when modelling fluid migration in geological formations. An increasing trend in recent years has been to use analogs to palliate this lack of knowledge, i.e., exploiting the spatial information from sites where the geology is accessible (outcrops, quarry sites) and transferring the observed properties to a study site deemed geologically similar. While this approach is appealing, it is difficult to put in place because of the lack of access to well-documented analog data. In this paper we present comprehensive analog data sets which characterize sedimentary structures from important groundwater hosting formations in Germany and Brazil. Multiple 2-D outcrop faces are described in terms of hydraulic, thermal and chemical properties and interpolated in 3-D using stochastic techniques. These unique data sets can be used by the wider community to implement analog approaches for characterizing reservoir and aquifer formations